Yinghua Wu*

Xin Chen, Yinghua Wu and Victor S. Batista

Department of Chemistry, Yale University, New Haven, CT 06520-8107

Xin Chen*Current address: Department of Chemistry, Tulane University.

Multidimensional Quantum Dynamics: Methods and Applications

Tuesday, September 28th, 2004 - Physical Chemistry Seminar 11:00 a.m., Room 1315 Chemistry Building Department of Chemistry, University of Wisconsin-Madison

Wcrest.gif

ESIPT in the keto-enolic tautomerization of 2-(2’-hydroxyphenyl)-oxazole (HPO).

Changes in hybridization and connectivityClassical Dynamics (HPMO)

Vendrell, O.; Moreno, M.; Lluch J.M.; Hammes-Schiffer, S. J. Phys. Chem. B 108, 6745 (2004)

Quantum Dynamics (7-d simulation, related ESIPT system)

Petkovic, M.; Kuhn, O. J. Phys. Chem. A 107, 8458 (2003)

SC-IVR (HPO)

Guallar, V.; Batista, V.S.; Miller, W.H. J. Chem. Phys. 113, 9510 (2000)Batista, V.S.; Brumer, P. Phys. Rev. Lett. 89, 143201 (2002) Batista, V.S.; Brumer, P. Phys. Rev. Lett. 89, 249903 (2002)

Computation of Observables

Time Dependent Reactant Population:

Absorption Spectrum:

Time Dependent Survival Amplitude

Reaction Surface 35-dimensional Model

V(r1,r2,z) = V0(r1,r2) + 1/2 [z- z0(r1,r2)] F(r1,r2) [z-z0(r1,r2)]

V0 : Reaction surface

z0 : ab initio geometries

F : ab initio force constants

r1,r2 : reaction coordinates

Reaction Coordinates in HPO

r1: H-stretching

Reaction Coordinates in HPO

r2: internal bending

CASSCF Reaction Surface Potential V0(r1,r2)

Time-Sliced Simulations of Quantum Processes

Wu,Y.; Batista, V.S. J. Chem. Phys. 118, 6720 (2003)Wu,Y.; Batista, V.S. J. Chem. Phys. 119, 7606 (2003)Wu,Y.; Batista, V.S. J. Chem. Phys. 121, 1676 (2004)Chen, X., Wu,Y.; Batista, V.S. J. Chem. Phys. submitted (2004)Wu,Y.; Batista, V.S. J. Chem. Phys. in prep. (2004)

MP/SOFT Method

Trotter Expansion

Time-Dependent Survival AmplitudeHK SC-IVR vs. MP/SOFT

Time-Dependent Survival Amplitude

HK SC-IVR vs. Classical Wigner

Wigner SC-IVR

Douhal et.al. JPC 100, 19789 (1997), HPMO in n-hexane

S1

S0

Comparison with experimental data

WIGNER, TD-SCF, HK SC-IVR, MP/SOFT

Time Dependent Reactant Population

Early Time Relaxation Dynamics

WIGNER, TD-SCF, HK SC-IVR, MP/SOFT

Time Dependent Reactant PopulationLonger Time Relaxation Dynamics

[1]

[2]

[2][1]Wu,Y.; Batista, V.S. J. Chem. Phys. in prep. (2004)Guallar, V.; Batista, V.S.; Miller, W.H. J. Chem. Phys. 113, 9510 (2000)

Time Dependent Reactant PopulationHK SC-IVR, Classical Wigner (SC/L) and WKB

Comparison with experimental data

Femtosecond fluorescent transient at 420nm for HPMO in 3-methylpentane JPC 102,1657 (1998) Zewail and co-workers

Time dependent reactant (enol) population

Decoherence DynamicsHK SC-IVR vs. MP/SOFT

Batista, V.S.; Brumer, P. Phys. Rev. Lett. 89, 143201 (2002)

[2]

[2]

[1]

[1]Wu,Y.; Batista, V.S. J. Chem. Phys. in prep. (2004)

Development of new methodologies for studies of Decoherence and Coherent-Control

Contour plot of the percentage product yield for bichromatic coherent-control at 100 fs after photoexcitation of the system, as a function of the laser controllable parameters.

Coherent-Control of the keto-enolic isomerization in HPO

Electron Tunneling in Multidimensional Systems

Wu,Y.; Batista, V.S. J. Chem. Phys. 121, 1676 (2004)

2-dimensional (Model I)

2-dimensional (Model I)

2-dimensional (Model I)

2-dimensional (model I)

5-dimensional (model I)

5-dimensional (model I)

5-dimensional (model I)

5-dimensional (model I)

5-dimensional (model I)

5-dimensional (model I)

5-dimensional (model I)

10-dimensional (model I)

Electron Tunneling in Multidimensional Systems

Model II

(2-dimension Model II)

2-dimensional (model II)

2-dimensional (model II)

2-dimensional (Model II)

20-dimensional (Model II)

20-dimensional (model II)

Benchmark calculation:

Thermal Correlation Functions

Boltzmann Ensemble Averages

Chen, X., Wu,Y.; Batista, V.S. J. Chem. Phys. submitted (2004)

Bloch Equation: MP/SOFT Integration

Partition Function Boltzmann Matrix:

Calculations of Thermal Correlation Functions

Time-Dependent Position Ensemble Average

Position-Position Correlation Function:

Model System:

Classical density

Quantum density

Ground State, V0

Excited State, V1

Model System, cont’d

Position-Position Correlation Function

Time-Dependent Position Ensemble Average

Conclusions

•We have introduced the MP/SOFT method for time-sliced simulations of quantum processes in systems with many degrees of freedom. The MP/SOFT method generalizes the grid-based SOFT approach to non-orthogonal and dynamically adaptive coherent-state representations generated according to the matching-pursuit algorithm. •The accuracy and efficiency of the resulting method were demonstrated in simulations of excited-state intramolecular proton transfer in 2-(2’-hydroxyphenyl)-oxazole (HPO), as modeled by an ab initio 35-dimensional reaction surface Hamiltonian, as well as in simulations of deep-tunneling quantum dynamics for systems with up to 20 coupled degrees of freedom. •Further, we have extended the MP/SOFT method for computations of thermal equilibrium density matrices (equilibrium properties of quantum systems), finite temperature time-dependent expectation values and time-correlation functions. The extension involves solving the Bloch equation via imaginary-time propagation of the density matrix in dynamically adaptive coherent-state representations, and the evaluation of the Heisenberg time-evolution operators through real-time propagation.

•NSF Career Award CHE#0345984•ACS PRF#37789-G6•NSF Nanoscale Exploratory Research (NER) Award ECS#0404191•Research Corporation, Innovation Award#RI0702•Hellman Family Fellowship•Anderson Fellowship•Yale University, Start-Up Package•NERSC Allocation of Supercomputer Time •Department of Chemistry, University of Wisconsin Madison

Thank you !

Acknowledgments